Let’s use the following variables:

- W = time taken to walk one way
- R = time taken to ride one way

From the problem statement, we know that:

- W + R = 6 hours 15 minutes = 6.25 hours (total time to walk a distance and ride back)
- 2W = 7 hours 45 minutes = 7.75 hours (total time to walk both ways)

We can use these equations to solve for R:

W + R = 6.25 2W = 7.75

Solving the second equation for W, we get:

W = 7.75 / 2 = 3.875 hours

Substituting this value of W into the first equation, we get:

3.875 + R = 6.25

Solving for R, we get:

R = 6.25 – 3.875 = 2.375 hours

Therefore, the time taken by him to ride back both ways is:

2R = 2 x 2.375 = 4.75 hours or 4 hours and 45 minutes